Cyclic time and recurrence: SMM/DTT and McTaggart’s A-series and B-series

01The question behind the comparison

A cycle repeats a configuration or operation; recurrence returns a system sufficiently close to an earlier state. Neither necessarily repeats the entire history. A clock hand can complete a turn while its counter advances. A biological rhythm can recur while the organism changes. SMM/DTT’s inner cycles can therefore coexist with an outer history that does not close. The key is to specify what cycles and what retains information from one completion to the next. Without that distinction, a circle in a diagram can misleadingly imply that all events recur exactly.

A compact inner variable may represent a periodic phase rather than a closed timelike curve in spacetime. Identifying phase values separated by a period is an algebraic or topological statement. It does not mean that a traveller returns to a past physical event. If a retained state changes after each traversal, the full state space includes both phase and memory. A projection onto phase alone then hides the accumulating history. This is especially useful for a theory that interprets stable matter as organized repetition: persistence can depend on a repeatable pattern without reducing the pattern’s biography to one closed orbit.

The six nested levels suggest cycles within cycles, but their periods need not be independent observables. A slower completion may require the successful closure of a lower operation. This structure can produce a hierarchy of effective timescales, although the values and ratios of those timescales still require dynamics. Counting six roles does not determine a frequency spectrum. A physical model would specify the recurrence condition, the stability of the cycle and the rule that carries memory between completions. These ingredients let cyclic generation support novelty rather than merely oppose it.

02The single-source and nested-time proposal

SMM begins with one nonspatial generative source. DTT distinguishes its inner production from the outer order in which completed results become accessible. The six inner levels are nested functional dependencies within that production; the seventh denotes outer completion. They are not six independent clocks, six spatial directions, or six simultaneously occupied temporal axes. This distinction makes the framework more specific than a general claim that everything changes: it asks how a world of persistent relations can be generated before its spatial representation is taken for granted. ^[2]

03The comparator’s explanatory structure

McTaggart distinguished tensed positions—past, present and future—from the relations earlier than and later than. His argument challenges the coherence of taking passage as a changing possession of incompatible temporal properties. For the comparison here, the distinction is a tool for asking what DTT’s completion adds to an ordered history. A sequence can be fully ordered without specifying which member is now present.

Consider a list of event labels A, B and C. The facts A precedes B and B precedes C do not change when a reader moves down the list. What changes is the reader’s relation to a particular entry. If a completion theory adds an objective change in actuality, it needs to say whether that change is another event, an irreducible feature of events, or a change in a meta-time. These alternatives expose the regress question without assuming that McTaggart’s conclusion is correct. His analysis is philosophical; it supplies no Hamiltonian, physical clock or information-processing mechanism. ^[1]

04The precise agreement and difference

A periodic sequence can be described using B-relations even though a display returns to the same value. McTaggart’s distinction helps reveal why recurrence of a property is not recurrence of the same temporal position. Noon on one day and noon on another have equal clock-face readings but different relations to surrounding events. DTT’s inner cycles therefore require a memory or history variable if outer succession is to remain distinguishable.

The A-series adds the question of which occurrence is present. A cycle in the generating mechanism does not answer that question by itself, nor does a circular diagram establish an eternal return. DTT’s distinctive contribution is the possibility that repeated inner closure produces new completed tokens carrying inherited relations. The full state is then a history-bearing process rather than a bare circle. This comparison makes the term cyclic precise: it can refer to an operation, a phase or an observable pattern while the event order remains open. It also prevents periodicity from being mistaken for a solution to the philosophical problem of passage. ^[1]

05Worked example: what follows and what does not

Consider a state (θ,m), with θ an angle and m an integer record count. One update advances θ by π/2; after four updates θ returns to its original value and m increases by one. The phase is periodic, but the full state is not. If an observer reads only cos θ, the display repeats every four steps. If the observer can also read m, successive cycles are distinguishable. This elementary model explains how circular inner organization and ordered outer history can coexist. It does not fix the physical duration of a cycle: assigning four milliseconds requires an additional clock relation, whereas four updates is only a count.

06What this comparison contributes

The strongest comparison focuses on identity across recurrences. Is a repeated form the same event, a new event with the same structure, or merely an observationally indistinguishable event? DTT’s language of renewed creation favors a new completion carrying inherited relations, but a particular model must state what is preserved. This perspective avoids treating recurrence as evidence for an eternal return of every experience while retaining the explanatory value of periodic organization.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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